Finite Normalized Tight Frames

By John J. Benedetto, Matthew C. Fickus. Advances in Computational Mathematics, 2003

488 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Signal Processing

View Paper: https://www.semanticscholar.org/paper/4a22529abad048e990dc5c80bbbd44d9b31f8016

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In Applied Mathematics

In Computer Vision and Pattern Recognition

In Signal Processing

Citations in the corpus

Minimization of the probabilistic p-frame potential (2010, background): “5 below was proved for the frame potential in [2], and we extend it to all p-frame potentials with 1 < p < ∞: Lemma 2.”
Ellipsoidal tight frames and projection decompositions of operators (2003, background): “Tight frames may be constructed having specified length, components having a predetermined sequence of norms, or with properties making them resilient to erasures. For examples, see [ 1 ], [2], [7], and [10].”
Designing structured tight frames via an alternating projection method (2005, background): “In words, minimizing the TSC is equivalent to ﬁnding a frame with prescribed column norms that is closest in Frobenius norm to a tight frame [52].”
RANK-ONE DECOMPOSITION OF OPERATORS AND CONSTRUCTION OF FRAMES (2003, background): “Introduction The existence and characterization of frames with a variety of additional properties is an area of active research which has resulted in recent papers including [1], [2], and [6].”
Gabor analysis over finite Abelian groups (2007, background): “Because these frames inherit symmetries from the groups they tend to have interesting extra properties.”
Frames for Undergraduates (2007, background): “[9] The minimum value of the frame potential for a set of k ≥ n unit vectors F = {xi}i=1 in an n-dimensional Hilbert space is k 2 n .”
Linear Independence of Finite Gabor Systems (2006, background): “We suggest [16], [24], [47], [109] as some interesting papers on “finite frames;” in particular, the last paper discusses links between finite frames and other areas such as discrete geometry and sphere packings.”
GRASSMANNIAN FRAMES WITH APPLICATIONS TO CODING AND COMMUNICATION (2003, background): “tight frames has recently been rediscovered in [ 3 ].”
The road to equal-norm Parseval frames (2010, background): “Despite their popularity, we know only a few ways to construct such frames analytically [23, 3, 9, 13], mostly with the help of group actions.”
A new identity for Parseval frames (2007, background): “In abstract frame theory, systems constituting tight frames and, in particular, Parseval frames have already been extensively explored [3, 6, 7, 10, 11, 12], yet many questions are still open.”
The Structure of Minimizers of the Frame Potential on Fusion Frames (2008, methodology): “Inspired by the work in classical frame theory (see [2, 18]), we study a convex functional on fusion frame operators (the FF potential or FFP), also studied in [8], which generalizes the Benedetto-Fickus frame potential.”
Tight Frames and Their Symmetries (2004, background): “Man y highly symmetric configuarations of vectors such as the n th roots of unity in IR 2 and the vertices of the platonic solids in I R 3 are known to be isometric tight frames with large symmetry groups (see eg. [ BF03 ]).”
Manifold structure of spaces of spherical tight frames (2003, background): “Some recent references on finite frame theory are [1]–[8] and [10].”